François-Xavier Vialard

Assistant Professor in Applied Mathematics at University Paris-Dauphine.

Address: Université Paris-Dauphine, CEREMADE UMR CNRS 7534, Place du Maréchal De Lattre De Tassigny
                75775 PARIS CEDEX 16 - FRANCE, Tel.: +33 (0)1 44-05-40-61

E-mail (remove ".nospam" and "nospam."):

Momentum scalar map on the surface of the brain

Research area

  • Analytical, geometrical and computational aspects of large deformation by diffeomorphisms (LDDMM)
  • Current research interests:

  • Generalization of optimal transport including growth. The Wasserstein-Fisher-Rao metric.
  • Connection between optimal transport metrics and fluid dynamics.
  • Higher-order models for large deformation by diffeomorphisms, optimal transport and their applications.

  • Other activities:
  • Member of the INRIA team MOKAPLAN, which aims at developing numerical algorithms and software to solve variational problems with a particular focus on optimal transport and its generalizations.
  • Member of the CNRS project CAVALIERI (défi Imag'in de la mission pour l'interdisciplinarité) together with Vincent Duval (PI) and Charles Dossal and Nicolas Papadakis and Julien Rabin. The goal is to develop new models and methods for applications in image analysis. For instance, developing new metrics for image comparison.
  • Co-organiser with Marc Hoffmann, Gabriel Peyré, Vincent Rivoirard of the Working Group Statistique et Imagerie at Paris-Dauphine.
  • Co-author with Laurent Risser and Darryl Holm as the Principal Investigator of the ERC granted project 2010: Five Grand Challenges in Computational Anatomy.

  • Preprints

  • Generalized compressible fluid flows and solutions of the Camassa-Holm variational model, T. Gallouet, A. Natale and F.-X. Vialard, 2018, Hal link.
  • Embedding Camassa-Holm equations in incompressible Euler, A. Natale and F.-X. Vialard, 2018, Hal link.
  • Variational Second-Order Interpolation on the Group of Diffeomorphisms with a Right-Invariant Metric, F.-X. Vialard, 2018, arXiv link.
  • Second order models for optimal transport and cubic splines on the Wasserstein space, J.D. Benamou, T. Gallouet, F.-X. Vialard, 2018, arXiv link.
  • Riemannian cubics on the group of diffeomorphisms and the Fisher-Rao metric, R. Tahraoui, F.-X. Vialard, 2016, arXiv link.

  • Journal papers:

  • Unbalanced Optimal Transport: Geometry and Kantorovich formulation, L. Chizat, B. Schmitzer, G. Peyré, F.-X. Vialard, accepted in JFA, arXiv link.
  • The Camassa-Holm as an incompressible Euler equation: A geometric point of view, T. Gallouët, F.-X. Vialard, accepted in Journal of Differential Equations 2017, arXiv link.
  • Quantum Optimal Transport for Tensor Field Processing, G. Peyré, L. Chizat, F.-X. Vialard, J. Solomon, accepted for publication in European Journal of Applied Mathematics, 2017, arXiv link.
  • Scaling Algorithms for Unbalanced Transport Problems, L. Chizat, B. Schmitzer, G. Peyré, F.-X. Vialard, accepted for publication in Mathematics of Computation, 2017, arXiv link.
  • An Interpolating Distance between Optimal Transport and Fisher-Rao distances, L. Chizat, B. Schmitzer, G. Peyré, F.-X. Vialard, accepted for publication in Foundations of Computational Mathematics 2016, arXiv link.
  • On Completeness of Groups of Diffeomorphisms, M. Bruveris and F.-X. Vialard, accepted for publication in JEMS, arXiv link.
  • A Second-order Total Variation Metric on the Space of Immersed Curves, G. Nardi, G. Peyré, F.-X. Vialard, accepted for publication, SIAM Imaging Science, arXiv link.
  • Finsler Steepest Descent with Applications to Piecewise-regular Curve Evolution, G. Charpiat, G. Nardi, G. Peyré, F.-X. Vialard, accepted for publication, Interfaces and Free Boundaries, arXiv link.
  • Splines for Diffeomorphisms, MedIA (Special issue for MICCAI), N.P. Singh, F.-X. Vialard, M. Niethammer, 2015. arXiv link.
  • Diffeomorphic Image Matching with Left-Invariant Metrics, Fields Institute Communications, Geometry, Mechanics, and Dynamics, The Legacy of Jerry Marsden, Tanya Schmah, Laurent Risser and F.-X. Vialard, 2014. arXiv link.
  • Longitudinal deformation models, spatial regularizations and learning strategies to quantify Alzheimer's disease progression. Neuroimage: Clinical, Fiot J.B., Raguet H., Risser L., Cohen L., Fripp J., Vialard F.X., 2014.
  • Bayesian Data Assimilation in Shape Registration, Inverse Problems, Cotter C.J. and Cotter S.L. and Vialard F.-X., 2012, eprint oxford.
  • Extension to Infinite Dimensions of a Stochastic Second-Order Model associated with the Shape Splines. Stochastic Processes and their Applications, 2012, doi. Also an arXiv link to a preliminary version of the work.
  • Piecewise-Diffeomorphic Image Registration: Application to the Motion Correction of 3D CT Lung Images using Sliding Conditions. Medical Image Analysis, Risser L., Vialard F.X., Baluwala H.Y., Schnabel J.A., 2012.
  • Mixture of Kernels and Iterated semidirect Product of Diffeomorphisms Groups. arXiv link (SIAM MMS) Bruveris M., Risser L., Vialard F.X., 2012.
  • Invariant higher-order variational problems II. arXiv link (Journal of Nonlinear Science) F. Gay-Balmaz, D. D. Holm, D. M. Meier, T. S. Ratiu and F.X. Vialard, 2012.
  • Invariant higher-order variational problems. arXiv link (Communications in Mathematical Physics - 2011) F. Gay-Balmaz, D. D. Holm, D. M. Meier, T. S. Ratiu and F.X. Vialard.
  • Diffeomorphic 3D Image Registration via Geodesic Shooting using an Efficient Adjoint Calculation. (IJCV)- 2011 Vialard F.X., Risser L., Rueckert D., Cotter C.J.
  • Simultaneous Multiscale Registration using Large Deformation Diffeomorphic Metric Mapping. (IEEE TMI - 2011) Risser L., Vialard F.X., Wolz R., Murgasova M., Holm D. and Rueckert D.
  • Shape Splines and Stochastic Shape Evolutions: A Second-Order Point of View. (pdf) (with Alain Trouvé, 2010, published in Quarterly of Applied Mathematics)
  • Extension de l'appariement d'images par difféomorphismes aux fonctions à variation bornée. (Note au C.R.A.S), with Filippo Santambrogio, 2008.
  • A semi-differentiation lemma on BV functions. (CVGMT website) (with Filippo Santambrogio, submitted, 2008)
  • Hamiltonian approach to geodesic image matching. (pdf) (working paper)

  • Conference papers:

  • Optimal Transport for Diffeomorphic Registration, J. Feydy, B. Charlier, F.-X. Vialard, G. Peyré, MICCAI 201, arXiv link.
  • Spatially-varying metric learning for diffeomorphic image registration. A variational framework. Vialard F.-X., Risser L. MICCAI 2014.
  • Left-invariant metrics for diffeomorphic image registration with spatially-varying regularisation. Schmah T., Risser L., Vialard F.-X., MICCAI 2013.
  • Riemannian metrics for statistics on shapes: Parallel transport and scale invariance. (pdf) M. Niethammer and F.-X. Vialard. MICCAI Workshop MFCA 2013, proceedings available on the website.
  • Local vs global descriptors of hippocampus shape evolution for Alzheimer's longitudinal population analysis. J.-B. Fiot, L. Risser, L. D. Cohen, J. Fripp, F.-X. Vialard. MICCAI Workshop STIA 2012.
  • Geodesic Regression. Niethammer M., Huang Y., Vialard F.-X., MICCAI 2011 (link to Marc Niethammer's webpage)
  • Construction of Diffeomorphic Spatio-temporal Atlases using Karcher means and LDDMM: Application to Early Cortical Development - Workshop on Image Analysis of Human Brain Development - (MICCAI-IAHBD 2011) - Risser L., Vialard F.X., Serag A., Aljabar P., Rueckert D.
  • Diffeomorphic Atlas Estimation using Karcher Mean and Geodesic Shooting on Volumetric Images. Medical Image Understanding and Analysis (MIUA'11). London, 2011. Vialard F.X., Risser L., Holm D.D., Rueckert D.
  • Large diffeomorphic registration using fine and coarse strategies. With L.Risser, F.X. Vialard, M.Murgasova, D.Rueckert and D.D.Holm, in the proceedings - Springer's LNCS of WBIR 2010.
  • A Second-Order Model for Time-Dependent Data Interpolation: Splines on Shape Spaces, Workshop Miccai 2010 STIA: Spatio-Temporal Image Analysis for Longitudinal and Time-Series Image Data, with A.Trouvé.
  • Simultaneous Fine and Coarse Diffeomorphic Registration: Application to the Atrophy Measurement in Alzheimer's Disease - proceedings Springer's LNCS of MICCAI 2010 (Beijing), L.Risser, F.X.Vialard, R.Wolz, D.D.Holm and D.Rueckert.
  • Coronary Motion Estimation Using Probability Atlas and Diffeomorphic Registration from CTA. International Workshop on Medical Imaging and Augmented Reality (MIAR'10) - Lecture Notes in Computer Science Beijing, 2010. Zhang D.P., Risser, L., Vialard F.X., Friman O., Neefjes L., Mollet N., Niessen W., Rueckert D.
  • Correlation, CDOs of ABS and the subprime crisis. With Frederic Patras and Jean-Pierre Lardy, published in Economica Eds: Christian Gourieroux and Monique Jeanblanc.

    Other notes and documents

  • On the Wasserstein-Fisher-Rao metric, F.-X. Vialard, 2015, pdf, Proceedings of Shape Analysis Workshop in Grundsund.
  • On the diffeomorphisms group generated by gaussian vector fields, F.-X. Vialard, 2014, pdf, Proceedings of Shape Analysis Workshop in Bad Gastein.
  • Notes of the course of Computational Anatomy using Geometric Mechanics available here. This document contains what I presented at the Geometry, Mechanics and Control 8th Intl. Young Researchers workshop 2013 held in Barcelona.
  • A notebook (julia) on the application of Anderson acceleration method to Sinkhorn algorithm (used in entropic regularization of optimal transport) for Brenier's multimarginal problem. AndersonMultiMarginal, html.

  • Software developed with Laurent Risser:

    uTIlzreg: Diffeomorphic registration of 3D images available on sourceforge. Some explanations about uTIlzreg are given here.

    A nice drawing

    HDR in 2017 - University Paris-Dauphine.

  • Title: Diffeomorphisms, Optimal Transport and Applications to Imaging. Pdf file.
  • PhD thesis in 2009 - ENS Cachan (Alain Trouvé was my advisor):

  • Hamiltonian Approach to Shape Spaces in a Diffeomorphic Framework : From the Discontinuous Image Matching Problem to a Stochastic Growth Model. HAL website
  • French title: Approche Hamiltonienne pour les espaces de formes dans le cadre des difféomorphismes: du recalage d'images discontinues à un modèle stochastique de croissance de formes

    Upcoming Talks:

    Past Talks:

  • New trends in applied geometric mechanics (D. Holm's' 70th birthday), ICMAT Madrid, July 2017.
  • Statistics and Shapes seminar, UNC, April 2017.
  • Medical Image Seminar, MIT, April 2017.
  • Shape, Image and Optimization, Muenster, March 2017.
  • Calculus of Variations and Optimal Transport (Brenier's 60th birthday), IHP, January 2017.
  • Journée transport optimal, équation de Monge-Ampère et applications (ANR Maga), IHES, December 2016.
  • GT CalVa, Orsay, October 2016.
  • MokaTAO meeting, Inria Paris, October 2016.
  • Geometric Measure Theory: Analysis and non-smooth objects, CIMI analysis semester, Toulouse, September 2016.
  • Mathematics of Shapes and Applications, Singapore, July 2016.
  • SIAM Imaging Science, Large Scale Inverse Problems in Medical Imaging, Albuquerque, May 2016.
  • Geometric analysis theory in vision and control conference, Voss - Bergen, May 2016.
  • Applied mathematics seminar, Cermics, ENPC, January 2016.
  • Geometric measure theory and its applications, ANR Geometrya, Grenoble, June 2015.
  • Bernoulli Institute, EPFL, April 2015.
  • Orsay university, applied analysis seminar, march 2015.
  • Infinite-Dimensional Riemannian Geometry with Applications to Image Matching and Shape Analysis in Vienna, February 2015.
  • FGMIA 2014, IHP.
  • ANR TOMMI, Grenoble, October 2013, slides.
  • Hamiltonian dynamics seminar, EPFL, October 2013.
  • Workshop MFCA, MICCAI Nagoya, September, 2013.
  • Séminaire de statistiques, IMT Toulouse, November, 2012.
  • FOCUS PROGRAM ON GEOMETRY, MECHANICS AND DYNAMICS the Legacy of Jerry Marsden, Fields Institute, July 2012.
  • Séminaire de statistiques, Université Paris 13, June, 2012.
  • ARC BrainVar (Cachan, Sept. 2007): "Approche Hamiltonienne pour le recalage d'image"
  • Workshop Geometry and statistics on shape spaces (Bonn, 2008): "Hamiltonian image matching"
  • Séminaire de mathematiques appliquées de Johns Hopkins University (Baltimore, Sept. 2008), "From the Hamiltonian image matching problem to a stochastic growth model."
  • Workshop on Shape spaces: (Annapolis, Avril 2009)
  • Soutenance de thèse (Cachan, Mai 2009)
  • CardioMaths seminar (Imperial College, Juin 2009)
  • Groupe de travail de mathématiques appliquées de l'ENS Cachan-Bretagne (Nov 2009).
  • Groupe de travail calcul des variations - Université Paris-Dauphine (March 2010).
  • Workshop on Computational Anatomy and mathematics on shape spaces - Imperial College (May 2010).
  • Workshop Miccai: Spatio-Temporal Image Analysis for Longitudinal and Time-Series Image Data - Beijing (September 2010).
  • AMSTAT Seminar of Warwick University, March 2011.
  • Groupe de travail, Université Paris 5 - Descartes, March 2011.
  • Workshop on Shape spaces: Imperial College London, 2011.
  • NatImages , IHP November 9th 2011.
  • SIGMA , Université Paris 6, November 18th, 2011.

  • Enseignements: (Teaching in french)

    Documents relatifs au cours d'optimisation numérique - L3 - Dauphine

  • Programme de l'examen 2014.
  • Voici le cours d'optimisation de L3.
  • Cette année, les TP se feront en utilisant le langage Python et les IPython Notebook afin de faciliter la rédaction et la correction des comptes rendus.
  • Voici une introduction à python produite avec les IPython Notebook.
  • Voici le lien vers le programme de l'examen 2013, les notes de cours et les TP/TD:
  • Le premier TD/TP 2014: TD/TP 1 et sa version html TD/TP 1. La nouvelle version du TP1.
  • Le TD sur l'algorithme de Barzilai et Borwein: TD 3
  • La suite du TD3: TD 3 - partie2
  • Le fichier python pour le TP 3: Masque.txt
  • Pour rendre les rapports et TPs: page des TP.
  • Image source.
  • micro1, micro2, micro3, micro4.
  • micro1_1, micro1_2.
  • OutilsSons.
  • Documents relatifs au cours d'algèbre linéaire 2 - DU1 - Dauphine - Mise a jour le Mercredi 24 fevrier 2016

  • Correction du CC2.
  • Programme de l'examen final'.
  • Document de cours contenant les preuves importantes.
  • Voici quelques TP développés pour la préparation à l'agrégation de l'ENS Cachan:

  • Une introduction à Matlab pour l'option A de l'agrégation de mathématiques (Probabilités et statistiques).
  • Un TP sur Monte-Carlo.
  • Un TP sur la gestion de stock.
  • Un TP sur les chaà®nes de Markov.

  • Divers:

  • Voici un développement original d'une petite question mathématique paru sous une forme enrichie dans la RMS (revue de la filière mathématique), revue pour les prépas et premières années d'université. Cette preuve de l'additivité géométrique d'une propriété analytique peut constituer un développement pour une leà§on d'agrégation sur les actions de groupes sur un ensemble.
  • Une note sur les isotopies. (pdf)
  • GMO detection statistical software OPACSA.
  • Mon mémoire de magistère. (pdf)


    papo y su combo, esta mochao.